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## STEM.M.MATHEMATICS: National Council of Teachers of Mathematics (NCTM)

MATHEMATICS: National Council of Teachers of Mathematics (NCTM)
NCTM.1. Number and Operations
1.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
1.1.1. Work flexibly with fractions, decimals, and percents to solve problems.
Flip Charts Applying Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Applications of percent
Quiz, Flash Cards, Worksheet, Game & Study Guide Applying Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Percent
Quiz, Flash Cards, Worksheet, Game & Study Guide Numbers and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

1.1.2. Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line.
Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions

1.1.3. Develop meaning for percents greater than 100 and less than 1.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Percent

1.1.4. Understand and use ratios and proportions to represent quantitative relationships.
Flip Charts Applying Percents
Flip Charts The Real Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Numbers and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Numerical Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

1.1.5. Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation.
Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

1.1.6. Use factors, multiples, prime factorization, and relatively prime numbers to solve problems.
Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions

1.1.7. Develop meaning for integers and represent and compare quantities with them.
Flip Charts The Real Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Integers

1.2. Understand meanings of operations and how they relate to one another.
1.2.1. Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

1.2.2. Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.
Flip Charts The Real Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Integers

1.2.3. Understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems.

1.3. Compute fluently and make reasonable estimates.
1.3.1. Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods.
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

1.3.2. Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Integers

1.3.4. Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.
Flip Charts Applying Percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Geometric Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Numbers and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Numerical Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

NCTM.11. Grade 8 Curriculum Focal Points
11.1. Algebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations
11.1.1. Students use linear functions, linear equations, and systems of linear equations to represent, analyze, and solve a variety of problems. They recognize a proportion (y/x = k, or y = kx) as a special case of a linear equation of the form y = mx + b, understanding that the constant of proportionality (k) is the slope and the resulting graph is a line through the origin. Students understand that the slope (m) of a line is a constant rate of change, so if the input, or x-coordinate, changes by a specific amount, a, the output, or y-coordinate, changes by the amount ma. Students translate among verbal, tabular, graphical, and algebraic representations of functions (recognizing that tabular and graphical representations are usually only partial representations), and they describe how such aspects of a function as slope and y-intercept appear in different representations. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines that intersect, are parallel, or are the same line, in the plane. Students use linear equations, systems of linear equations, linear functions, and their understanding of the slope of a line to analyze situations and solve problems.
Flip Charts Slope
Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

11.2. Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle
11.2.1. Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem

11.3. Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets
11.3.1. Students use descriptive statistics, including mean, median, and range, to summarize and compare data sets, and they organize and display data to pose and answer questions. They compare the information provided by the mean and the median and investigate the different effects that changes in data values have on these measures of center. They understand that a measure of center alone does not thoroughly describe a data set because very different data sets can share the same measure of center. Students select the mean or the median as the appropriate measure of center for a given purpose.
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data
Quiz, Flash Cards, Worksheet, Game & Study Guide Organizing Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

NCTM.12. Connections to the Grade 8 Focal Points
12.1. Algebra: Students encounter some nonlinear functions (such as the inverse proportions that they studied in grade 7 as well as basic quadratic and exponential functions) whose rates of change contrast with the constant rate of change of linear functions. They view arithmetic sequences, including those arising from patterns or problems, as linear functions whose inputs are counting numbers. They apply ideas about linear functions to solve problems involving rates such as motion at a constant speed.
Flip Charts Circle Around
Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Nonlinear Functions and Set Theory
Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences

12.2. Geometry: Given a line in a coordinate plane, students understand that all 'slope triangles' - triangles created by a vertical 'rise' line segment (showing the change in y), a horizontal 'run' line segment (showing the change in x), and a segment of the line itself - are similar. They also understand the relationship of these similar triangles to the constant slope of a line.
Flip Charts Slope
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

12.3. Data Analysis: Building on their work in previous grades to organize and display data to pose and answer questions, students now see numerical data as an aggregate, which they can often summarize with one or several numbers. In addition to the median, students determine the 25th and 75th percentiles (1st and 3rd quartiles) to obtain information about the spread of data. They may use box-and-whisker plots to convey this information. Students make scatterplots to display bivariate data, and they informally estimate lines of best fit to make and test conjectures.
Quiz, Flash Cards, Worksheet, Game & Study Guide Analyzing, Graphing and Displaying Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
Quiz, Flash Cards, Worksheet, Game & Study Guide Organizing Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

12.4. Number and Operations: Students use exponents and scientific notation to describe very large and very small numbers. They use square roots when they apply the Pythagorean Theorem.
Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents
Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem

NCTM.2. Algebra
2.1. Understand patterns, relations, and functions.
2.1.1. Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
Flip Charts Circle Around
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences

2.2. Represent and analyze mathematical situations and structures using algebraic symbols.
2.2.1. Develop an initial conceptual understanding of different uses of variables.
Flip Charts Algebra Skills
Flip Charts Applying Percents
Flip Charts Inequalities
Flip Charts Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

2.2.2. Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.
Flip Charts Slope
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Nonlinear Functions and Set Theory

2.2.3. Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

2.2.4. Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra

2.3. Use mathematical models to represent and understand quantitative relationships.
2.3.1. Model and solve contextualized problems using various representations, such as graphs, tables, and equations.
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Equations

2.4. Analyze change in various contexts.
2.4.1. Use graphs to analyze the nature of changes in quantities in linear relationships.
Quiz, Flash Cards, Worksheet, Game & Study Guide Nonlinear Functions and Set Theory

NCTM.3. Geometry
3.1. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
3.1.1. Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.
Flip Charts Dot to Dot
Flip Charts Finding Volume
Flip Charts Perimeter & Area
Flip Charts Plane Geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Finding Volume
Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Closed Figure Relationships
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Lines and Angles
Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

3.1.2. Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.
Quiz, Flash Cards, Worksheet, Game & Study Guide Geometric Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

3.1.3. Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
Flip Charts Plane Geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Geometric Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Closed Figure Relationships
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Lines and Angles
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem

3.2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
3.2.1. Use coordinate geometry to represent and examine the properties of geometric shapes.
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

3.2.2. Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides.
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

3.3. Apply transformations and use symmetry to analyze mathematical situations.
3.3.1. Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

3.3.2. Examine the congruence, similarity, and line or rotational symmetry of objects using transformations.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

3.4. Use visualization, spatial reasoning, and geometric modeling to solve problems.
3.4.4. Use geometric models to represent and explain numerical and algebraic relationships.
Flip Charts Dot to Dot
Flip Charts Finding Volume
Flip Charts Perimeter & Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Finding Volume
Quiz, Flash Cards, Worksheet, Game & Study Guide Measurement, Perimeter, and Circumference
Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area
Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

NCTM.4. Measurement
4.1. Understand measurable attributes of objects and the units, systems, and processes of measurement.
4.1.3. Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume.
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Lines and Angles

4.2. Apply appropriate techniques, tools, and formulas to determine measurements.
4.2.2. Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.
Flip Charts Algebra Skills
Flip Charts Dot to Dot
Flip Charts Finding Volume
Flip Charts Perimeter & Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Finding Volume
Quiz, Flash Cards, Worksheet, Game & Study Guide Measurement, Perimeter, and Circumference
Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Lines and Angles
Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

4.2.3. Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.
Flip Charts Dot to Dot
Flip Charts Perimeter & Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Measurement, Perimeter, and Circumference
Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area

4.2.4. Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders.
Flip Charts Finding Volume
Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Finding Volume
Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

4.2.5. Solve problems involving scale factors, using ratio and proportion.
Quiz, Flash Cards, Worksheet, Game & Study Guide Geometric Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

4.2.6. Solve simple problems involving rates and derived measurements for such attributes as velocity and density.
Quiz, Flash Cards, Worksheet, Game & Study Guide Numerical Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

NCTM.5. Data Analysis and Probability
5.1. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
5.1.1. Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population.
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

5.1.2. Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.
Quiz, Flash Cards, Worksheet, Game & Study Guide Analyzing, Graphing and Displaying Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

5.2. Select and use appropriate statistical methods to analyze data.
5.2.1. Find, use, and interpret measures of center and spread, including mean and interquartile range.
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Organizing Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

5.2.2. Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.
Quiz, Flash Cards, Worksheet, Game & Study Guide Analyzing, Graphing and Displaying Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

5.3. Develop and evaluate inferences and predictions that are based on data.
5.3.2. Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit.
Quiz, Flash Cards, Worksheet, Game & Study Guide Analyzing, Graphing and Displaying Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

5.3.3. Use conjectures to formulate new questions and plan new studies to answer them.
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

5.4. Understand and apply basic concepts of probability
5.4.2. Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations.
Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Probability

5.4.3. Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models.
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Probability

NCTM.6. Problem Solving
6.1. Build new mathematical knowledge through problem solving.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

6.2. Solve problems that arise in mathematics and in other contexts.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

6.3. Apply and adapt a variety of appropriate strategies to solve problems.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

NCTM.7. Reasoning and Proof
7.1. Recognize reasoning and proof as fundamental aspects of mathematics.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

7.2. Make and investigate mathematical conjectures.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

7.3. Develop and evaluate mathematical arguments and proofs.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

7.4. Select and use various types of reasoning and methods of proof.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

NCTM.9. Connections
9.2. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

Science